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formal statement (Lean)
102private theorem logicNatLift_unique_fun (B : PeanoObject)
103 (f : PeanoObject.Hom logicNatPeano B) :
104 f.toFun = (logicNatLift B).toFun := by
proof body
Tactic-mode proof.
105 funext n
106 induction n with
107 | identity =>
108 exact f.map_zero
109 | step n ih =>
110 calc
111 f.toFun (LogicNat.step n) = B.step (f.toFun n) := f.map_step n
112 _ = B.step ((logicNatLift B).toFun n) := by rw [ih]
113 _ = (logicNatLift B).toFun (LogicNat.step n) := rfl
114
115/-- `LogicNat` is initial among Peano objects. -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (12)
Lean names referenced from this declaration's body.
-
step
in IndisputableMonolith.Complexity.CellularAutomata
decl_use
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LogicNat
in IndisputableMonolith.Foundation.ArithmeticFromLogic
decl_use
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Hom
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
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logicNatLift
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
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logicNatPeano
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
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PeanoObject
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
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identity
in IndisputableMonolith.Foundation.ObserverForcing
decl_use
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is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
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is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
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is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
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is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
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identity
in IndisputableMonolith.RRF.Foundation.VantageCategory
decl_use